Exam 9: Hypothesis Testing

A Type I error is rejecting a true null hypothesis.

In a bottling process,a manufacturer will lose money if the bottles contain either more or less than is claimed on the label.Suppose a quality manager for a steak sauce company is interested in testing whether the mean number of ounces of steak sauce per restaurant-size bottle differs from the labeled amount of 20 ounces.The manager samples nine bottles,measures their contents,and finds the sample mean is 19.7 ounces and the sample standard deviation is 0.3 ounces.Test the hypotheses at α = .05.

We are testing H₀: ? ? 8;versus H_A: ? > 8.Given ? = .01,n = 25, $\bar { X } = 8.112$ and s = .16,we should reject the H₀.(Assume the sample is selected from a normally distributed population. )

In 1930,the average size of a public restroom was 172 square feet.By 1990,due to federal disability laws,the average size had increased to 471 square feet.Suppose that a design team believes that this standard has increased from the 1990 level.They randomly sample 23 public restrooms in a major midwestern city and obtain a mean square footage of 498.78 with a standard deviation of 46.94.Calculate the appropriate test statistic to test the hypotheses.

The manufacturer of an over-the-counter heartburn relief mediation claims that its product brings relief in less than 3.5 minutes,on average.To be able to make this claim,the manufacturer was required by the FDA to present statistical evidence in support of the claim.The manufacturer reported that for a sample of 50 heartburn sufferers,the mean time to relief was 3.3 minutes and the population standard deviation was 1.1 minutes.Calculate the p-value that corresponds to the test statistic.

Everything else being constant,increasing the sample size decreases the probability of committing a Type II error.

____________ is the probability of not rejecting H₀ when H₀ is false.

A major car manufacturer wants to test a new catalytic converter to determine whether it meets new air pollution standards.The mean emission of all converters of this type must be less than 20 parts per million of carbon.Ten (10)converters are manufactured for testing purposes and their emission levels are measured,with a mean of 17.17 and a standard deviation of 2.98.Calculate the appropriate test statistic to test the hypotheses.

Failure to meet payments on student loans guaranteed by the US government has been a major problem for both banks and the government.Approximately 50 percent of all student loans guaranteed by the government are in default.A random sample of 350 loans to college students in one region of the United States indicates that 147 are in default.Calculate the p-value associated with the test statistic,and test the hypothesis that the selected region's default rate is lower than the national percentage at α = .01.

When conducting a hypothesis test about a single mean,reducing the level of significance (α)will increase the size of the rejection region.

The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription.The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions.To test her theory,she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle.She finds a sample mean of 62.05 and a standard deviation of 4.45.Calculate a confidence interval to test the hypotheses at α = .002 and interpret the result.

We test H₀: ? ? 3.0;versus H_A: ? > 3.0.If $\bar { X } = 3.44$ s = .57,and n = 13,at a significance level of .05,we do not reject H₀.(Assume population normality. )

In an early study,researchers at Ivy University found that 33 percent of the freshmen had received at least one A in their first semester.Administrators are concerned that grade inflation has caused this percentage to increase.In a more recent study,of a random sample of 500 freshmen,185 had at least one A in their first semester.Calculate the p-value associated with the test statistic and test the claim at α = .05.

When 100 randomly selected car owners are surveyed,it is found that the mean length of time they plan to keep their car is 7.01 years,and the population standard deviation is 3.74 years.Calculate the p-value for the test statistic used to test the claim that the mean years for all car owners is less than 7.5 years,and determine whether the null hypothesis can be rejected at α = .05.

The manager of a local specialty store is concerned with a possible slowdown in payments by her customers.She measures the rate of payment in terms of the average number of days receivables are outstanding.Generally,the store has maintained an average of 50 days with a standard deviation of 10 days.A random sample of 25 accounts gives an average of 54 days outstanding with a standard deviation of 8 days.Calculate the appropriate test statistic to test the hypotheses.

A major airline company is concerned that its proportion of late arrivals has substantially increased in the past month.Historical data shows that on the average 18% of the company airplanes have arrived late.In a random sample of 1,240 airplanes,310 airplanes have arrived late.If we are conducting a hypothesis test of a single proportion to determine if the proportion of late arrivals has increased: What is the value of the calculated test statistic?

It has been hypothesized that on average employees spend one hour a day playing video games at work.To test this at her company,a manager takes a random sample of 35 employees,who showed a mean time of 55 minutes per day,with an assumed population standard deviation of 5 minutes.Calculate the test statistic.

The university registrar claims that fewer than 20 percent of the students who enroll at Ivy University graduate in four years.To test this claim,a random sample of 100 students was selected,and 18 were found to have graduated in four years.Calculate the p-value associated with the test statistic and test the claim at α = .05.

If a one-sided null hypothesis is rejected at a given significance level,then the corresponding two-sided null hypothesis (i.e. ,the same sample size,the same standard deviation,and the same mean)will ______________ be rejected at the same significance level.

A survey of the wine market has shown that the preferred wine for 17 percent of Americans is merlot.A wine producer in California,where merlot is produced,believes the figure is higher in California.She contacts a random sample of 550 California residents and asks which wine they purchase most often.Suppose 115 replied that merlot was the primary wine.Calculate the p-value associated with the test statistic,and test the claim at α = .01.